Math Problem Statement

For the following linear system: x + y - z = 1, 2x + 3y + k*z = 3, x + k*y + 3z = 2. Find the value(s) of k for which the system has: (i) no solution, (ii) unique solution, (iii) infinite solutions.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Systems of Linear Equations
Matrices and Determinants

Formulas

Determinant of a matrix: det(A) = Σ (product of elements and their cofactors)
Condition for unique solution: det(A) ≠ 0
Condition for infinite/no solution: det(A) = 0 and rank conditions

Theorems

Cramer's Rule
Rank-Nullity Theorem

Suitable Grade Level

Grades 11-12